2021/03/22 by M. El Guide, Guide, M. El, Alaa El Ichi +5 · 5 citations
Computer Science · Engineering · Mathematics · Physics and Astronomy · #65F10 #65F22 #Algebra over a field #Algorithm #Applied mathematics #Artificial intelligence #Cartesian tensor #Computer science #Discrete cosine transform #Electromagnetic Scattering and Analysis #Exact solutions in general relativity #FOS: Mathematics #Generalized minimal residual method #Image (mathematics) #Krylov subspace #Linear system #Mathematical analysis #Mathematics #Numerical Analysis (math.NA) #Pure mathematics #Sparse and Compressive Sensing Techniques #Symmetric tensor #Tensor (intrinsic definition) #Tensor contraction #Tensor decomposition and applications #Tensor density #Tensor field #Tensor product #Tensor product of Hilbert spaces #cs.NA #math.NA #msc:65F10 #msc:65F22
paper · pdf · doi:10.48550/arxiv.2103.11847
published in arXiv (Cornell University) (Cornell University) · arXiv admin note: text overlap with arXiv:2006.07133
arxiv created 2021/03/22 · openalex publication_date 2021/03/22 · arxiv updated 2021/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the present work, we propose new tensor Krylov subspace method for ill posed linear tensor problems such as in color or video image restoration. Those methods are based on the tensor-tensor discrete cosine transform that gives fast tensor-tensor product computations. In particular, we will focus on the tensor discrete cosine versions of GMRES, Golub-Kahan bidiagonalisation and LSQR methods. The presented numerical tests show that the methods are very fast and give good accuracies when solving some linear tensor ill-posed problems.